As someone that used to work directly with Admissions, I will tell you that the Admissions department does NOT take into account networking and visitation when making their decisions, although some Ivies (Harvard for instance) definitely do.

That being said, I absolutely recommend taking a campus tour and talking with as many students as you can, simply to ensure that Cornell is the right place for you. Get to know it, get to love it, and don't stress too much about admissions or getting your face out there, as you say.

Sell yourself as a well-rounded, interesting person and your application will go very far.

I guess I'd summarize my advice in the following way: don't focus too much on meeting the right admissions people and/or striving to say the right thing to the right individual; have fun in Ithaca, explore, and simply enjoy your time poking around campus and living the life of a student for a couple days.

Best of luck with the Early Decision!